Approximation Of Quasi-Differential Operators In VTI Media And Its Applications

Seismic wave propagation in anisotropic models is important for exploration geophysics and seismology.Anisotropy in sedimentary rocks presents the feature of isotropy in the transverse direction and inhomogeneity in the vertical direction,known as transversely isotropic media(TI media).Alkhalifa get a qP-wave governing equation of TI media in order to reducing the calculation of full-wave equation in TI media.In addition,Existing qP-wave equations suffer terrible qSV-wave residual which is disadvantage for our study.This thesis present a simple and useful qP-wave governing equation by using the average square approximation and Pade approximation onto qP-wave dispersion relation derived by Thomsen(1986)in vertical transverse isotropy(VTI)to overcome qSV-wave residual.For title transverse isotropy(TTI)implementation,this thesis get a pure qP wave equation of average square approximation of TTI media by rotating coordinate.Numerical results demonstrate that the proposed equation is much more accuracy and effective.The numerical wavefields generated by this equation are very clear without qSV-residual.Also,this article showed the effectiveness and steadiness of our equation with numerical examples with complicated three-layer model and Hess/Salt model.All of these show that the proposed equation can be used to simulate qP-wave propagation in anisotropic media.This research provide a new way for seismic wave simulation in TTI media,which can have important theoretical meaning and application value.